Various methods and apparatus have been provided for purposes of protecting persons who work, or otherwise find themselves, at dangerous heights. In some situations, including elevator shafts, for example, a vertical cable is available as a suitable structure for anchoring a safety device. Generally speaking, it is desirable to secure a safety device to such a cable in a manner which allows a person to move along the cable or lock onto the cable at his discretion, and which automatically locks onto the cable and/or remains locked onto the cable in the event of a fall or an excessively rapid descent. It is also desirable for such a safety device to engage cables of various diameters and/or in a manner which does not damage the cables.